Bifurcations in heart rhythms

Heart rhythms exhibit the following interesting phenomena: First, rhythmic cells such as sinus node cells cease their rhythmic activity when a single brief current pulse of the right magnitude is given to the cell at the right time. Second, a premature pulse can initiate a tachycardia (i.e., reentrant arrhythmia) from a quiescent atrial tissue. This tachycardia can be sustained for hours until another brief current pulse is given. Third, ECG recording sometimes shows alternans in electrical activity prior to ventricular tachycardia. Some suggested that this alternans is the first bifurcation in a period doubling sequence. Fourth, a certain class of antiarrhythmic drugs may increase the chance of sudden cardiac death for patients with a history of myocardial infarction. Fifth, when an ''adjustable'' tricuspid ring is shortened, the conduction velocity of a reentrant wave becomes oscillatory. When the ring size is shortened further, reentry terminates after several oscillatory cycles. Sixth, sustained reentry arises in a tricuspid ring when Class IC drugs (i.e., which exclusively block the sodium channel) are added. On the other hand, Class III (which exclusively blocks the potassium channel) can terminate sustained reentry in the tricuspid ring. In this tutorial review, we explain how one can utilize a bifurcation analysis to explain all these interesting phenomena involved in heart rhythms.